Below are the truth tables for the different logical operators. They will all use the variables p and q in each table.
LOGICAL AND
Requires that BOTH sides of the statement have T for their truth value in order to make the statement true.
LOGICAL OR
Requires that 1 or BOTH sides of the statement have T for their truth value in order to make the statement true.
LOGICAL NOT
Simply negates the logic. True becomes false and false becomes true.
| p | q | !p | !q |
| T | T | F | F |
| T | F | F | T |
| F | T | T | F |
| F | F | T | T |
LOGICAL NOR (Not OR)
Simply the negation of the OR truth table.
| p | q | p NOR q |
| T | T | F |
| T | F | F |
| F | T | F |
| F | F | T |
LOGICAL NAND (Not And)
Simply the negation of the AND truth table.
| p | q | p NAND q |
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | T |
LOGICAL IMPLIES
Simply means if p is T than q is T, as an example.
LOGICAL EQUIVALENCE
Simply a double implication. If p -> q is T and q -> p is T, than the whole statement is true (as an example). You must perform the implications twice, hence the double arrow.
| p | q | p <-> q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |